Interface coupling of independently modeled structural and other multiphysics computational modules is emerging as a key procedure for local refinements, contact-impact modeling, and parallel simulation employing partitioned domains. In the first part of this paper, we present a localized version of the method of Lagrange multipliers whose key feature is the use of frames that lie between the partitioned domains and that facilitate localized interface coupling as opposed to global coupling inherent when employing the classical method of Lagrange multipliers. In the second part of the paper we present a selection of its applications to the coupling of non-matching interfaces and contact problems. In particular, we present an interface patch test criterion that can be employed a priori for the construction of patch test-passing interfaces. The resulting coupling procedure satisfies a priori the interface patch test when the interfaces are discretized with different non-matching meshes. Example are finally discussed, which demonstrate the utility of the present method as compared to the master-slave method, the mortar method and the so-called three-field method.